Nicholas P. Schafer

AWSEM-MD: protein structure prediction using coarse-grained physical potentials and bioinformatically based local structure biasing.

The associative memory, water mediated, structure and energy model (AWSEM) is a coarse-grained protein force field. AWSEM contains physically motivated terms, such as hydrogen bonding, as well as a bioinformatically based local structure biasing term, which efficiently takes into account many-body effects that are modulated by the local sequence. When combined with appropriate local or global alignments to choose memories, AWSEM can be used to perform de novo protein structure prediction. Herein we present structure prediction results for a particular choice of local sequence alignment method based on short residue sequences called fragments. We demonstrate the models structure prediction capabilities for three levels of global homology between the target sequence and those proteins used for local structure biasing, all of which assume that the structure of the target sequence is not known. When there are no homologues in the database of structures used for local structure biasing, AWSEM calculations produce structural predictions that are somewhat improved compared with prior works using related approaches. The inclusion of a small number of structures from homologous sequences improves structure prediction only marginally, but when the fragment search is restricted to only homologous sequences, AWSEM can perform high resolution structure prediction and can be used for kinetics and dynamics studies.

Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection

Significance Natural protein sequences, being the result of random mutation coupled with natural selection, have remarkable properties that are not typical of unselected random sequences, including the ability to robustly fold to an organized structure that is needed to function. We estimate the selection temperature, the effective temperature at which sequences were selected by evolution, for eight protein families and compare these values with experimental data for folding temperatures of proteins in each family. The selection temperature measures the importance of maintaining the stability and structural specificity of the folded state on the evolutionary process. For all families, the selection temperature is below physiological temperature, indicating that maintaining the structural integrity of the folded state is an important constraint on evolution. The energy landscape used by nature over evolutionary timescales to select protein sequences is essentially the same as the one that folds these sequences into functioning proteins, sometimes in microseconds. We show that genomic data, physical coarse-grained free energy functions, and family-specific information theoretic models can be combined to give consistent estimates of energy landscape characteristics of natural proteins. One such characteristic is the effective temperature Tsel at which these foldable sequences have been selected in sequence space by evolution. Tsel quantifies the importance of folded-state energetics and structural specificity for molecular evolution. Across all protein families studied, our estimates for Tsel are well below the experimental folding temperatures, indicating that the energy landscapes of natural foldable proteins are strongly funneled toward the native state.

Frustration in the energy landscapes of multidomain protein misfolding

Frustration from strong interdomain interactions can make misfolding a more severe problem in multidomain proteins than in single-domain proteins. On the basis of bioinformatic surveys, it has been suggested that lowering the sequence identity between neighboring domains is one of nature’s solutions to the multidomain misfolding problem. We investigate folding of multidomain proteins using the associative-memory, water-mediated, structure and energy model (AWSEM), a predictive coarse-grained protein force field. We find that reducing sequence identity not only decreases the formation of domain-swapped contacts but also decreases the formation of strong self-recognition contacts between β-strands with high hydrophobic content. The ensembles of misfolded structures that result from forming these amyloid-like interactions are energetically disfavored compared with the native state, but entropically favored. Therefore, these ensembles are more stable than the native ensemble under denaturing conditions, such as high temperature. Domain-swapped contacts compete with self-recognition contacts in forming various trapped states, and point mutations can shift the balance between the two types of interaction. We predict that multidomain proteins that lack these specific strong interdomain interactions should fold reliably.

Free energy landscapes for initiation and branching of protein aggregation

Significance This study leverages a predictive protein-folding simulation model to study the free energy landscapes of fused oligomeric constructs to quantify the conditions under which these constructs spontaneously misfold. Constructs of this type have been used to probe the early stages of aggregation in the laboratory. Oligomeric species may be the toxic agents in misfolding-related diseases. The critical structures that initiate aggregation are shown to depend on specific sequence signals and thermodynamic conditions. Our results also suggest that branching due to the presence of multiple amyloidogenic segments may determine the morphology of protein aggregates. Experiments on artificial multidomain protein constructs have probed the early stages of aggregation processes, but structural details of the species that initiate aggregation remain elusive. Using the associative-memory, water-mediated, structure and energy model known as AWSEM, a transferable coarse-grained protein model, we performed simulations of fused constructs composed of up to four copies of the Titin I27 domain or its mutant I27* (I59E). Free energy calculations enable us to quantify the conditions under which such multidomain constructs will spontaneously misfold. Consistent with experimental results, the dimer of I27 is found to be the smallest spontaneously misfolding construct. Our results show how structurally distinct misfolded states can be stabilized under different thermodynamic conditions, and this result provides a plausible link between the single-molecule misfolding experiments under native conditions and aggregation experiments under denaturing conditions. The conditions for spontaneous misfolding are determined by the interplay among temperature, effective local protein concentration, and the strength of the interdomain interactions. Above the folding temperature, fusing additional domains to the monomer destabilizes the native state, and the entropically stabilized amyloid-like state is favored. Because it is primarily energetically stabilized, the domain-swapped state is more likely to be important under native conditions. Both protofibril-like and branching structures are found in annealing simulations starting from extended structures, and these structures suggest a possible connection between the existence of multiple amyloidogenic segments in each domain and the formation of branched, amorphous aggregates as opposed to linear fibrillar structures.

Funneling and frustration in the energy landscapes of some designed and simplified proteins

We explore the similarities and differences between the energy landscapes of proteins that have been selected by nature and those of some proteins designed by humans. Natural proteins have evolved to function as well as fold, and this is a source of energetic frustration. The sequence of Top7, on the other hand, was designed with architecture alone in mind using only native state stability as the optimization criterion. Its topology had not previously been observed in nature. Experimental studies show that the folding kinetics of Top7 is more complex than the kinetics of folding of otherwise comparable naturally occurring proteins. In this paper, we use structure prediction tools, frustration analysis, and free energy profiles to illustrate the folding landscapes of Top7 and two other proteins designed by Takada. We use both perfectly funneled (structure-based) and predictive (transferable) models to gain insight into the role of topological versus energetic frustration in these systems and show how they differ from those found for natural proteins. We also study how robust the folding of these designs would be to the simplification of the sequences using fewer amino acid types. Simplification using a five amino acid type code results in comparable quality of structure prediction to the full sequence in some cases, while the two-letter simplification scheme dramatically reduces the quality of structure prediction.

Protein Frustratometer 2: A tool to localize energetic frustration in protein molecules now with electrostatics

The protein frustratometer is an energy landscape theory-inspired algorithm that aims at localizing and quantifying the energetic frustration present in protein molecules. Frustration is a useful concept for analyzing proteins’ biological behavior. It compares the energy distributions of the native state with respect to structural decoys. The network of minimally frustrated interactions encompasses the folding core of the molecule. Sites of high local frustration often correlate with functional regions such as binding sites and regions involved in allosteric transitions. We present here an upgraded version of a webserver that measures local frustration. The new implementation that allows the inclusion of electrostatic energy terms, important to the interactions with nucleic acids, is significantly faster than the previous version enabling the analysis of large macromolecular complexes within a user-friendly interface. The webserver is freely available at URL: http://frustratometer.qb.fcen.uba.ar.

Electrostatics, structure prediction, and the energy landscapes for protein folding and binding

While being long in range and therefore weakly specific, electrostatic interactions are able to modulate the stability and folding landscapes of some proteins. The relevance of electrostatic forces for steering the docking of proteins to each other is widely acknowledged, however, the role of electrostatics in establishing specifically funneled landscapes and their relevance for protein structure prediction are still not clear. By introducing Debye‐Hückel potentials that mimic long‐range electrostatic forces into the Associative memory, Water mediated, Structure, and Energy Model (AWSEM), a transferable protein model capable of predicting tertiary structures, we assess the effects of electrostatics on the landscapes of thirteen monomeric proteins and four dimers. For the monomers, we find that adding electrostatic interactions does not improve structure prediction. Simulations of ribosomal protein S6 show, however, that folding stability depends monotonically on electrostatic strength. The trend in predicted melting temperatures of the S6 variants agrees with experimental observations. Electrostatic effects can play a range of roles in binding. The binding of the protein complex KIX‐pKID is largely assisted by electrostatic interactions, which provide direct charge‐charge stabilization of the native state and contribute to the funneling of the binding landscape. In contrast, for several other proteins, including the DNA‐binding protein FIS, electrostatics causes frustration in the DNA‐binding region, which favors its binding with DNA but not with its protein partner. This study highlights the importance of long‐range electrostatics in functional responses to problems where proteins interact with their charged partners, such as DNA, RNA, as well as membranes.

Cooperative folding of a polytopic α-helical membrane protein involves a compact N-terminal nucleus and nonnative loops.

Significance How a protein folds in a membrane is a problem of central biological significance. Although extensively investigated for globular proteins, there are very limited data available for membrane proteins due to the difficulties of finding a tractable model system. We present a study of the folding of a six-transmembrane helix protein, the rhomboid protease GlpG, which folds according to a two-state model in a membrane-mimicking mixed micelle surfactant system. By recording the kinetics of folding and unfolding of 69 GlpG mutants and performing an extensive ϕ-value analysis, we propose a folding mechanism and discuss its possible interpretations and implications. These data serve as an excellent starting point for computational studies of membrane protein folding mechanisms and kinetics. Despite the ubiquity of helical membrane proteins in nature and their pharmacological importance, the mechanisms guiding their folding remain unclear. We performed kinetic folding and unfolding experiments on 69 mutants (engineered every 2–3 residues throughout the 178-residue transmembrane domain) of GlpG, a membrane-embedded rhomboid protease from Escherichia coli. The only clustering of significantly positive ϕ-values occurs at the cytosolic termini of transmembrane helices 1 and 2, which we identify as a compact nucleus. The three loops flanking these helices show a preponderance of negative ϕ-values, which are sometimes taken to be indicative of nonnative interactions in the transition state. Mutations in transmembrane helices 3–6 yielded predominantly ϕ-values near zero, indicating that this part of the protein has denatured-state–level structure in the transition state. We propose that loops 1–3 undergo conformational rearrangements to position the folding nucleus correctly, which then drives folding of the rest of the domain. A compact N-terminal nucleus is consistent with the vectorial nature of cotranslational membrane insertion found in vivo. The origin of the interactions in the transition state that lead to a large number of negative ϕ-values remains to be elucidated.

Discrete Kinetic Models from Funneled Energy Landscape Simulations

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.

Predictive energy landscapes for folding α-helical transmembrane proteins

Significance The understanding of how membrane proteins fold pales in comparison with the understanding of globular protein folding. This discrepancy is partly due to the fact that membrane proteins are difficult to work with experimentally. In turn, the lack of high-quality experimental data has caused modeling of membrane proteins to lag behind. Also, the extent to which the translocon assists transmembrane domains in folding is unclear. The number of experimentally determined membrane protein structures has recently increased, and we may now be at the stage where it has become possible to derive transferable simulation models for studying transmembrane protein folding. We describe the optimization of one such model and its application to predicting helical packings within the native topology. We explore the hypothesis that the folding landscapes of membrane proteins are funneled once the proteins’ topology within the membrane is established. We extend a protein folding model, the associative memory, water-mediated, structure, and energy model (AWSEM) by adding an implicit membrane potential and reoptimizing the force field to account for the differing nature of the interactions that stabilize proteins within lipid membranes, yielding a model that we call AWSEM-membrane. Once the protein topology is set in the membrane, hydrophobic attractions play a lesser role in finding the native structure, whereas polar–polar attractions are more important than for globular proteins. We examine both the quality of predictions made with AWSEM-membrane when accurate knowledge of the topology and secondary structure is available and the quality of predictions made without such knowledge, instead using bioinformatically inferred topology and secondary structure based on sequence alone. When no major errors are made by the bioinformatic methods used to assign the topology of the transmembrane helices, these two types of structure predictions yield roughly equivalent quality structures. Although the predictive energy landscape is transferable and not structure based, within the correct topological sector we find the landscape is indeed very funneled: Thermodynamic landscape analysis indicates that both the total potential energy and the contact energy decrease as native contacts are formed. Nevertheless the near symmetry of different helical packings with respect to native contact formation can result in multiple packings with nearly equal thermodynamic occupancy, especially at temperatures just below collapse.